MAYBE * Step 1: PolyRank MAYBE + Considered Problem: Rules: 0. f2(A,B) -> f2(-1 + A,B) [B >= 0 && A >= 1] (?,1) 1. f0(A,B) -> f2(C,-1 + B) [B >= 1] (1,1) 2. f2(A,B) -> f2(C,-1 + B) [B >= 0 && B >= 1 && 0 >= A] (?,1) Signature: {(f0,2);(f2,2)} Flow Graph: [0->{0,2},1->{0,2},2->{0,2}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f0) = x2 p(f2) = 1 + x2 Following rules are strictly oriented: [B >= 0 && B >= 1 && 0 >= A] ==> f2(A,B) = 1 + B > B = f2(C,-1 + B) Following rules are weakly oriented: [B >= 0 && A >= 1] ==> f2(A,B) = 1 + B >= 1 + B = f2(-1 + A,B) [B >= 1] ==> f0(A,B) = B >= B = f2(C,-1 + B) * Step 2: Failure MAYBE + Considered Problem: Rules: 0. f2(A,B) -> f2(-1 + A,B) [B >= 0 && A >= 1] (?,1) 1. f0(A,B) -> f2(C,-1 + B) [B >= 1] (1,1) 2. f2(A,B) -> f2(C,-1 + B) [B >= 0 && B >= 1 && 0 >= A] (B,1) Signature: {(f0,2);(f2,2)} Flow Graph: [0->{0,2},1->{0,2},2->{0,2}] + Applied Processor: Failing "Open problems left." + Details: Open problems left. MAYBE